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Generalizing the concept of primary fields, we find a new representation of the
Virasoro algebra, which we call pseudo-conformal representation. In special
cases, this representation reduces to ordinary- or logarithmic-conformal field
theory. There are, however, other cases in which the Green functions differ
from those of ordinary- or logarithmic-conformal field theories. This
representation is parametrized by two matrices. We classify these two matrices,
and calculate some of the correlators for a simple example.
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